Annulus (mathematics)

In Mathematics , an annulus (the Latin word for "little ring", with plural ''annuli'') is a ring-shaped geometric figure, or more generally, a term used to name a ring-shaped object. The adjective form is '''annular''' (for example, an Annular Eclipse ).

The open annulus is Topologically Equivalent to the open Cylinder

S^1 	imes (0,1)

.

The area of such an annulus is given by the difference in the areas of a Circle of radius ''R'' and one of radius ''r'':
:

A = \pi(R^2 - r^2)\,

This result can be obtained via Calculus by dividing the annulus up into an infinite number of annuli of Infinitesimal width

d
ho

and area

2\pi
ho d
ho

( = circumference × width) and then Integrating from

ho = r

ho = R

:
:

A = \int_r^R 2\pi
ho\, d
ho = \pi(R^2-r^2).

Interestingly, the area of an annulus can also be obtained by multiplying pi by the square of half of the length of the longest interval that can lie completely inside the annulus.

COMPLEX STRUCTURE

In Complex Analysis an annulus ''ann(a; r, R)'' in the Complex Plane is an Open Region defined by:

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Annulus (mathematics)